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New classes of exact solutions to general nonlinear equations and systems of equations in mathematical physics. (English) Zbl 1217.35166

From the text: New classes of exact solutions to some general nonlinear equations and systems of equations of mathematical physics are described that involve arbitrary functions. Special attention is given to equations and systems of equations encountered in the theory of mass and heat transfer, mathematical biology, and wave theory.

In this paper, an exact solution is regarded in the sense of the definition given in [A. D. Polyanin, V. F. Zaitsev and A. I. Zhurov, Methods for solving nonlinear equations in mathematical physics and mechanics. Fizmatlit, Mowcow, (2005)], page 10.

35Q53KdV-like (Korteweg-de Vries) equations
35Q79PDEs in connection with classical thermodynamics and heat transfer
35Q92PDEs in connection with biology and other natural sciences
35C05Solutions of PDE in closed form
80A20Heat and mass transfer, heat flow
35A24Methods of ordinary differential equations for PDE